The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks

Jain, Shashi; Oosterlee, Cornelis W.

doi:10.1016/j.amc.2015.07.085

Cited by 83 publications

(119 citation statements)

References 22 publications

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“…The other reason is due to the use of the "regress-later technique" in our algorithm. When we implement this technique, one condition is that the conditional expectations of the basis functions should be known analytically, see Jain and Oosterlee (2015) and Cong and Oosterlee (2015). If we choose other basis functions, the conditional expectations may not be directly available and therefore the accuracy of the "regress-later technique" may be affected negatively.…”

mentioning

confidence: 99%

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On pre-commitment aspects of a time-consistent strategy for a mean-variance investor

Cong

Oosterlee

2016

Journal of Economic Dynamics and Control

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a b s t r a c tIn this paper, a link between a time-consistent and a pre-commitment investment strategy is established. We define an implied investment target, which is implicitly contained in a time-consistent strategy at a given time step and wealth level. By imposing the implied investment target at the initial time step on a time-consistent strategy, we form a hybrid strategy which may generate better mean-variance efficient frontiers than the time-consistent strategy. We extend the numerical algorithm proposed in Cong and Oosterlee (2016b) to solve constrained time-consistent mean-variance optimization problems. Since the time-consistent and the pre-commitment strategies generate different terminal wealth distributions, time-consistency is not always inferior to pre-commitment.

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confidence: 99%

“…In general, we can deal with this problem by using a large number of simulations, which is however expensive. In our numerical approach we use the so-called "regress-later technique", as applied in Jain and Oosterlee (2015) and Oosterlee (2016a, 2016b).…”

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confidence: 99%

On pre-commitment aspects of a time-consistent strategy for a mean-variance investor

Cong

Oosterlee

2016

Journal of Economic Dynamics and Control

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“…SGBM employs bundling to approximate the conditional distribution using simulation. The method samples this distribution by bundling the grid points at t m−1 and then uses those paths that originate from the corresponding bundle to obtain a conditional sample for time t m , see also in [17]. Different approaches for partitioning can be considered.…”

Section: Stochastic Grid Bundling Methodsmentioning

confidence: 99%

“…The SGBM [17] is a simulation-based MC method for pricing early-exercise options (such as Bermudan options). SGBM first generates MC paths forward in time, followed by determining the optimal early-exercise policy, moving backwards in time in a dynamic programming framework, based on the Bellman principle of optimality.…”

Section: Stochastic Grid Bundling Methodsmentioning

confidence: 99%

“…One of the recent simulation-regression pricing techniques for early-exercise (Bermudan) options with several underlying assets, on which we will focus, is the stochastic grid bundling method (SGBM), proposed by Jain and Oosterlee [17]. The method is a hybrid of regression and bundling approaches, as it employs regressed value functions, together with bundling of the state space to approximate continuation values at different time steps.…”

Section: Introductionmentioning

confidence: 99%

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GPU acceleration of the stochastic grid bundling method for early-exercise options

Leitao

Oosterlee

2015

International Journal of Computer Mathematics

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In this work, a parallel graphics processing units (GPU) version of the Monte Carlo stochastic grid bundling method (SGBM) for pricing multi-dimensional early-exercise options is presented. To extend the method's applicability, the problem dimensions and the number of bundles will be increased drastically. This makes SGBM very expensive in terms of computational costs on conventional hardware systems based on central processing units. A parallelization strategy of the method is developed and the general purpose computing on graphics processing units paradigm is used to reduce the execution time. An improved technique for bundling asset paths, which is more efficient on parallel hardware is introduced. Thanks to the performance of the GPU version of SGBM, a general approach for computing the early-exercise policy is proposed. Comparisons between sequential and GPU parallel versions are presented.

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Towards control of dam and reservoir systems with forward–backward stochastic differential equations driven by clustered jumps

Yoshioka

2022

Adv Control Appl

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We deal with a new maximum principle‐based stochastic control model for river management through operating a dam and reservoir system. The model is based on coupled forward–backward stochastic differential equations (FBSDEs) derived from jump‐driven streamflow dynamics and reservoir water balance. A continuous‐time branching process with immigration driven by a tempered stable subordinator efficiently describes clustered inflow streamflow dynamics. This is a completely new attempt in hydrology and control engineering. Applying a stochastic maximum principle to the dynamics based on an objective functional for designing cost‐efficient control of dam and reservoir systems leads to the FBSDEs as a system of optimality equations. The FBSDEs under a linear‐quadratic ansatz lead to a tractable model, while they are solved numerically in the other cases using a least‐squares Monte‐Carlo method. Optimal controls are found in the former, while only sub‐optimal ones are computable in the latter due to a hard state constraint. Model parameters are successfully identified from a real data of a river in Japan having a dam and reservoir system. We also show that the linear‐quadratic case can capture the real operation data of the system with underestimation of the outflow discharge. More complex cases with a realistic time horizon are analyzed numerically to investigate impacts of considering the environmental flows and seasonal operational purposes. Key challenges towards more sophisticated modeling and analysis with jump‐driven FBSDEs are discussed as well.

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The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks

Cited by 83 publications

References 22 publications

On pre-commitment aspects of a time-consistent strategy for a mean-variance investor

On pre-commitment aspects of a time-consistent strategy for a mean-variance investor

GPU acceleration of the stochastic grid bundling method for early-exercise options

Towards control of dam and reservoir systems with forward–backward stochastic differential equations driven by clustered jumps

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